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The equation of the chord of contact of the point $(4, 2)$ with respect to the circle $x^{2} + y^{2} - 5 x + 4 y - 3 = 0$ is

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$x - 14 y - 6 = 0$

$3 x + 8 y - 18 = 0$

$8 x - 2 y - 11 = 0$

$5 x - 3 y - 25 = 0$

answer is C.

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Detailed Solution

$S_{1} = 0 \Rightarrow x x_{1} + y y_{1} - \frac{5}{2} (x + x_{1}) + 2 (y + y_{1}) - 3 = 0$

$\Rightarrow 4 x + 2 y - \frac{5}{2} (x + 4) + 2 (y + 2) - 3 = 0$

$3 x + 8 y - 18 = 0$

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